GMM Results
Lauren White
6/28/2020
Methods
Study Site and Study Species
The study was conducted from July 23 to October 29, 2019 in a population of carp (Cyprinus carpio) in Parley Lake, Lake Town Township (44°52’51.8“N 93°43’54.1”W). Carp were captured and PIT tagged across whole lake. Two PIT tag sites were established along the western coast of Parley Lake: Boat Ramp and Crown College (Fig #). The Upper part of Parley Lake, north of Crown College, has more dense aquatic vegetation. The lower part consists of more open water.
This experiment proceeded in these phases: pre-baiting, baiting, and removal. Antennas were set up and activated for data recording at both sites starting July 23, 2019. Baiting began at both sites on July 30, 2019. Nets were installed on August 16, 2019. The first capture attempt occurred on August 19, 2020. Here we conservatively analyze the period between when baiting began and when the first net was installed (July 30-August 16, 2020).
Data Collection
In total, 305 carp were captured and PIT tagged in Lake Parley for the 2019 season. PIT tag stations collected data every __ of a second. Each site consisted of three separate antenna positioned 5 m apart (Fig with diagram of individual site set up). At the Boat Ramp and Crown College sites, 99 and 107 unique fish were detected respectively. 70 and 75 of these fish were also detected during the baiting phase respectively.
## [1] 304## [1] 99## [1] 107## [1] 70## [1] 75Results
Number of visits through time
Below we show the number of visits through time for both the Boat Ramp and Crown College sites. The three blue lines in the histogams below indicate the dates of baiting, adding nets, and the first capture event respectively. 
In these plots, individual visits of unique carp are shown through time. Individual antenna within each site are shown in different colors illustrating the continuous, temporal data that has been collected. Interpretation These plots suggests that individual carp may have independent preferences for certain antenna within a site and that these preferences may be malleable/plastic through time. Some daytime vs. night time cycling is also visible, with activity typically clustered in evening and morning hours.
Superfeeders and feeding preference
Below we show histograms for the number of sampling days each fish visits Boat Ramp and Crown college. Interpretation While the majority of sampled individuals (>20 at both Boat Ramp and Crown College sites) are detected only once, there is a long tail distribution, which resemble a power law distribution. This suggests that there are a few individuals which are consistently present at either site.
We also combine visits by site and show the relative proportion of visits to each site per fish. We highlight “superfeeders”–those fish accounting for the top 20% of total visits to the left of the vertical black line. Interpretation this plots suggest, that in general, but particularly for superfeeders, that carp have strong site fidelity/preference for a particular site.
Average group size and feeding bout duration
Below we show histograms for average group size during feeding for the Boat Ramp and Crown College sites, as detected by Gaussian mixed models (GMM).
Interpretation: Smaller associations/shoaling events are more common. For the Boat Ramp site with antennas disaggregated, the mean duration of feeding bouts is 10.2 min and the median duration is 6.1 min. Group size vs. bout duration plots for both ways of analyzing Boat Ramp data seems to suggest that larger groups/feeding bouts are generally shorter than smaller group associations.
## bout groupsize dur dur_min
## 1 1 3 46 0.7666667
## 2 2 3 417 6.9500000
## 3 3 2 150 2.5000000
## 4 4 2 377 6.2833333
## 5 5 2 436 7.2666667
## 6 6 2 301 5.0166667
## [1] 10.22216## [1] 6.116667
Interpretation: For the Boat Ramp site with antennas aggregated, the mean duration of feeding bouts is 6.3 min and the median duration is 4.1 min. As with disaggregated antenna above, larger groups usually associate for less time comparatively.
## bout groupsize dur dur_min
## 1 1 3 114 1.900000
## 2 2 2 121 2.016667
## 3 3 4 323 5.383333
## 4 4 3 223 3.716667
## 5 5 5 400 6.666667
## 6 6 2 483 8.050000
## [1] 6.347634## [1] 4.066667
Interpretation: For the Crown College site with antennas disaggregated, the mean duration of feeding bouts is 10.1 min and the median duration is 6.1 min. Larger groups usually associate for less time comparatively.
## bout groupsize dur dur_min
## 1 1 3 672 11.200000
## 2 2 2 1616 26.933333
## 3 3 3 167 2.783333
## 4 4 6 557 9.283333
## 5 5 4 348 5.800000
## 6 6 3 371 6.183333
## [1] 10.12148## [1] 6.166667
Interpretation: For the Crown College site with antennas aggregated, the mean duration of feeding bouts is 6.0 min and the median duration is 4.8 min. Larger groups usually associate for less time comparatively.
## bout groupsize dur dur_min
## 1 1 5 496 8.266667
## 2 2 5 176 2.933333
## 3 3 2 68 1.133333
## 4 4 3 281 4.683333
## 5 5 2 341 5.683333
## 6 6 2 643 10.716667
## [1] 5.964779## [1] 4.783333
Interpretation: For Lake Parley with antennas disaggregated, the mean duration of feeding bouts is 10.2 min and the median duration is 5.8 min. Larger groups usually associate for less time comparatively.
## bout groupsize dur dur_min
## 1 1 2 219 3.650000
## 2 2 3 214 3.566667
## 3 3 2 316 5.266667
## 4 4 2 208 3.466667
## 5 5 2 70 1.166667
## 6 6 2 484 8.066667
## [1] 10.23019## [1] 5.783333
Interpretation: For Lake Parley with antennas aggregated, the mean duration of feeding bouts is 6.1 min and the median duration is 4.5 min. Larger groups usually associate for less time comparatively.
## bout groupsize dur dur_min
## 1 1 2 87 1.4500000
## 2 2 3 60 1.0000000
## 3 3 2 201 3.3500000
## 4 4 3 63 1.0500000
## 5 5 3 150 2.5000000
## 6 6 2 44 0.7333333
## [1] 6.131006## [1] 4.516667
GMM Networks
Here we show plots of individual networks derived from aggregated and disaggregated antenna for Boat Ramp, Crown College, and both sites togther. This code also produced histograms of weighted degree which reflects both the number of edges (contacts) of a given node, but also the frequency or intensity of those interactions.
Interpretation: Across the sites,like the superfeeder histogram plots above, we see something resembling a powerlaw distribution where most individuals have a low weighted degree, but fewer have higher numbers and intensities of interactions.
In the weighted degree vs. betweenness plots, we see that some indvidiuals have an especially high betweenness and/or weighted degree score relative to the rest of the population. This points to potential social influencers
Boat Ramp Networks
## Generating 70 x 70 matrix
## Warning: Removed 5 rows containing missing values (geom_point).
## Generating 70 x 70 matrix
## Warning: Removed 4 rows containing missing values (geom_point).
Crown College Networks
## Generating 75 x 75 matrix
## Warning: Removed 7 rows containing missing values (geom_point).
## Generating 75 x 75 matrix
## Warning: Removed 5 rows containing missing values (geom_point).
Lake Parley Networks
## Generating 107 x 107 matrix
## Warning: Removed 4 rows containing missing values (geom_point).
## Generating 107 x 107 matrix
## Warning: Removed 5 rows containing missing values (geom_point).
Boxplots of individual network measures
Here we plot boxplots of individual unweighted degree, overall association strength (weighted degree) and betweenness for networks of Boat Ramp, College Crown, and the combined sites.
Interpretation: It’s difficult to interpret the first few boxplots (across different types of metrics) because the scale of the different metrics is so different (e.g. betweenness with scores up to 400 and local transitivity which scales from 0 to 1). The last box plot looks at the effect of aggregated or separating the antenna at any given site across network metrics. We see that combining antenna generally leads to higher betweenness and weighted degree scores, although not a stastically significant level. What I read from this is that we’re not necessarily losing anything or changing much by aggregating vs. disaggregating antenna. Although the combined Lake Parley analysis certainly points to some individuals as “connecting” the two sites with outlier betweenness scores.
## Warning: Removed 5 rows containing non-finite values (stat_boxplot).
## Warning: Removed 4 rows containing non-finite values (stat_boxplot).
## Warning: Removed 7 rows containing non-finite values (stat_boxplot).
## Warning: Removed 7 rows containing non-finite values (stat_boxplot).
## Warning: Removed 4 rows containing non-finite values (stat_boxplot).
## Warning: Removed 5 rows containing non-finite values (stat_boxplot).
## Warning: Removed 30 rows containing non-finite values (stat_boxplot).
Reproducibility
## [1] "2020-06-28 15:10:20 EDT"## Local: master /research-home/lwhite/Carp
## Remote: master @ origin (https://github.com/whit1951/Carp.git)
## Head: [841802b] 2020-02-24: Initial attempt to look at network metrics through time## R version 4.0.1 (2020-06-06)
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## attached base packages:
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## [25] coda_0.19-3 evaluate_0.14 labeling_0.3 knitr_1.29
## [29] parallel_4.0.1 Rcpp_1.0.4.6 scales_1.1.1 farver_2.0.3
## [33] hms_0.5.3 digest_0.6.25 stringi_1.4.6 grid_4.0.1
## [37] tools_4.0.1 magrittr_1.5 maps_3.3.0 tibble_3.0.1
## [41] cluster_2.1.0 crayon_1.3.4 pkgconfig_2.0.3 MASS_7.3-51.6
## [45] ellipsis_0.3.1 prettyunits_1.1.1 rmarkdown_2.3 R6_2.4.1
## [49] git2r_0.27.1 nlme_3.1-148 compiler_4.0.1References
Damien R. Farine (2019). asnipe: Animal Social Network Inference and Permutations for Ecologists. R package version 1.1.12. https://CRAN.R-project.org/package=asnipe
Social Networks and Data Analysis
We created social networks using the Gaussian mixture model approach (Psorakis et al., 2012, 2015). Rather than establishing an arbitrary time threshold to detect social associations, this approach identifies high density activity periods in order to determine group associations. These analyses were carried out in the
asnipepackage using thegmmeventsfunction to identify temporal group associations from the PIT tag data and theget_networkfunction to create a network from the resulting group-by-individual matrix (Farine, 2019).Here we focused on the two sites that were running simultaneously in July and August of 2019: Boat Ramp and Crown College. For both these sites, the first day of corn baiting took place on July 30, 2019, nets were installed, August 16, 2020, and the first capture attempt took place August 19, 2020. Although antenna within a given site are near each other, we compared GMM analyses were visits were disaggregated by antenna vs. disaggregated by site. We also compared individual sites (Boat Ramp and Crown College) with both sites aggregated together (Lake Parley).